## Odd Function Problem

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
burnbird16
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### Odd Function Problem

Yet another problem for your brilliant minds to ponder!

Simplify (f(x+h) - f(x))/h, where f(x) = 2x+3

Here's what I did, please tell me if I made an error.

2(x+h) +3 - 2x - 3 / h

2x + 2h + 3 - 2x - 3 /h

2h/h

2

Thank you for your help!

Martingale
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### Re: Odd Function Problem

Yet another problem for your brilliant minds to ponder!

Simplify (f(x+h) - f(x))/h, where f(x) = 2x+3

Here's what I did, please tell me if I made an error.

2(x+h) +3 - 2x - 3 / h

2x + 2h + 3 - 2x - 3 /h

2h/h

2

Thank you for your help!
You really need to use parentheses or do this...

$\frac{2(x+h) +3 - (2x + 3)} { h}$

$\frac{2x+2h +3 - 2x - 3} { h}$

$\frac{2h} { h}=2$

burnbird16
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### Re: Odd Function Problem

I'm sorry, but I don't know how to do what you just did.

Martingale
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### Re: Odd Function Problem

I'm sorry, but I don't know how to do what you just did.

$\frac{2(x+h) +3 - (2x + 3)} { h}$

$\frac{2x+2h +3 - 2x - 3} { h}$

$\frac{2h} { h}=2$

Code: Select all

$$\frac{2(x+h) +3 - (2x + 3)} { h}$$ $$\frac{2x+2h +3 - 2x - 3} { h}$$ $$\frac{2h} { h}=2$$

Martingale
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### Re: Odd Function Problem

you could have also did it this way...

[2(x+h) +3 - 2x - 3] / h

=[2x + 2h + 3 - 2x - 3]/h

=2h/h

=2

for h not equal to zero

burnbird16
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### Re: Odd Function Problem

Ok, thank you. So was I correct,then? If so, I have a few more I would like for you to look at, if you have time.

Martingale
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### Re: Odd Function Problem

Ok, thank you. So was I correct,then? If so, I have a few more I would like for you to look at, if you have time.
Your final answer is correct but your notation is not. Your really need to put in brackets or parentheses.

Martingale
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### Re: Odd Function Problem

... I have a few more I would like for you to look at, if you have time.
I'll be on for a little while...and I'm sure there are others here that can also help with this.

burnbird16
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### Re: Odd Function Problem

Of course, and I will do so, thank you very much ^^

However, I do have a few more problems that I need some help with.

I'll just list them off, as I don't even know how to start any of them.

30. a) The graph of a quadratic function has x-intercepts, -1 and 3, and a range consisting of all numbers less than or equal to 4. Determine an expression for the function. (I tried to reverse factor, but I got a positive parabola, not a negative one.)

31. Write as a single equation in x and y: x = t + 1, y = $t^2+t$

34. Express x in terms of the other variables in this picture: http://www.flickr.com/photos/46210274@N07/4918073428/ (I drew it myself, I know it's kind of small, but it is a replica of the drawings in the packet)

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
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### Re: Odd Function Problem

...
30. a) The graph of a quadratic function has x-intercepts, -1 and 3, and a range consisting of all numbers less than or equal to 4. Determine an expression for the function. (I tried to reverse factor, but I got a positive parabola, not a negative one.)
...

for this your function needs to look like...

$f(x)=k(x+1)(x-3)$

since you want the range to be less than or equal to 4 we know the parabola goes down so $k<0$

by symmetry the max will occur at x=1 (the middle of -1 and 3)

so plug 1 into the function and solve for k (ie solve $f(1)=4$)

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